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Multidimensional Hele‐Shaw flows modelling Stokesian fluids
Author(s) -
Escher Joachim,
Matioc BogdanVasile
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1053
Subject(s) - mathematics , hele shaw flow , compressibility , surface tension , flow (mathematics) , mathematical analysis , mechanics , geometry , physics , thermodynamics , open channel flow
We consider here an n ‐dimensional periodic flow describing the motion of an incompressible Stokesian fluid in a Hele‐Shaw cell. The free surface separating the fluid from air, at pressure normalized to be zero, is moving under the influence of gravity and surface tension. We prove the existence of a unique classical Hölder solution for small perturbations of cylinders. Moreover, we evidence the existence of a single steady state and prove its exponential stability. Copyright © 2008 John Wiley & Sons, Ltd.